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Chapter 6: Q.39 (page 386)
About what percent of values lie between the first and second standard deviations from the mean (both sides)?
About of the values from normal distribution will lie between first and second standard deviation.
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What is the z-score of x= –, if it is standard deviations to the right of the mean?
IQ is normally distributed with a mean of and a standard deviation of . Suppose one individual is randomly chosen. Let of an individual.
a.
b. Find the probability that the person has an IQ greater than . Include a sketch of the graph, and write a probability statement
c. MENSA is an organization whose members have the top of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. Sketch the graph, and write the probability statement.
d. The middle of IQs fall between what two values? Sketch the graph and write the probability statement.
The heights of the National Basketball Association players were listed on team rosters at the start of the season. The heights of basketball players have an approximately normal distribution with mean, inches and a standard deviation, inches. For each of the following heights, calculate the z-score and interpret it using complete sentences
a. inches
b. inches
c. If an NBA player reported his height had a z-score of , would you believe him? Explain your answer
In China, four-year-olds average three hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.5 hours and the amount of time spent alone is normally distributed. We randomly select one Chinese four-year-old living in a rural area. We are interested in the amount of time the child spends alone per day.
a. In words, define the random variable X.
b. X ~ _____(_____,_____)
c. Find the probability that the child spends less than one hour per day unsupervised. Sketch the graph, and write the probability statement.
d. What percent of the children spend over ten hours per day unsupervised?
e. Seventy percent of the children spend at least how long per day unsupervised?
Suppose has a normal distribution with mean and standard deviation of five. Between what values of do of the values lie
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